Question

Two pillars are $120ft$ apart and the height of one is double that of the other. From the middle point of the line joining their feet, an observer finds that the angular elevations of their tops are complementary. The height of the longer tower is:

• A. $35\sqrt{2}$ ft
• B. $60\sqrt{2}$ ft
• C. $50\sqrt{2}$ ft
• D. $40\sqrt{2}$ ft

Answer 1

The correct option is B $60\sqrt{2}$ ft

$\tan \theta =\frac{h}{d}$
$\Rightarrow \tan (90-\theta )=\frac{h}{2d}$

=>$\cot \theta =\frac{h}{2d}$
$\Rightarrow \frac{h^2}{2d^2}=1$
$\Rightarrow h=d\sqrt{2}$
$\Rightarrow h=60\sqrt{2}ft$